Problem: Simplify the following expression: $\sqrt{150} - \sqrt{24}$
Solution: First, try to factor any perfect squares out of the radicals. $= \sqrt{150} - \sqrt{24}$ $= \sqrt{25 \cdot 6} - \sqrt{4 \cdot 6}$ Separate the radicals and simplify. $= \sqrt{25} \cdot \sqrt{6} - \sqrt{4} \cdot \sqrt{6}$ $= 5\sqrt{6} - 2\sqrt{6}$ Finally, simplify by combining the terms. $= ( 5 - 2 )\sqrt{6} = 3\sqrt{6}$